A topological method to characterize tapped granular media from the position of the particles

摘要

We use the first Betti number of a complex to characterize the morphologicalstructure of granular samples in mechanical equilibrium. We analyzetwo-dimensional granular packings after a tapping process by means of bothsimulations and experiments. States with equal packing fraction obtained withdifferent tapping intensities are distinguished after the introduction of afiltration parameter which determines the particles (nodes in the network) thatare joined by an edge. We first use numerical simulations to characterize theeffect of the precision in the particles localization by artificially addingdifferent levels of noise in this magnitude. The outcomes obtained for thesimulations are then compared with the experimental results allowing a cleardistinction of experimental packings that have the same density. This isaccomplished by just using the position of the particles and no otherinformation about the possible contacts, or magnitude of forces.